A coalition of Republican senators, including rising stars such as Rand Paul of Kentucky and Marco Rubio of Florida, have joined forces to push a school voucher bill that’s sure to draw fierce opposition from the White House and congressional Democrats.

The legislation, introduced by Mr. Paul and veteran GOP Sen. Lamar Alexander of Tennessee on Thursday, would allow more than $14 billion in federal Title 1 dollars to follow students to the school of their choice, whether it be a public, charter or private institution.

Up to $1,300 in Title 1 money, funneled from the federal government to more than half of the nation’s schools and earmarked for low-income children, would be available for 11 million students across the nation.

Senate Minority Leader Mitch McConnell of Kentucky, Mr. Rubio of Florida and Sen. Pat Toomey of Pennsylvania are co-sponsoring the measure, the latest Republican attempt to expand education vouchers.

“School choice for low-income parents and students across America is a way out of the poverty cycle,” Mr. Paul said in a statement. “Allowing Title 1 funds to follow the student creates an opportunity for students to get the most out of their education in the best environment possible.”

But school voucher programs have historically met intense resistance from most Democrats, who argue that they divert money from cash-strapped public schools while offering government financing of private — often religious — schools. The Obama administration, led by Education Secretary Arne Duncan,  repeatedly has expressed its opposition to the notion. The nation’s teachers unions also have routinely blasted such proposals.

Republicans counter that school-choice measures represent smart economics at a time when education spending is expected to fall dramatically as a result of the recent sequestration spending cuts.

“When dollars intended to help low-income children are diverted to other purposes, we deprive these children of their opportunity to attend a better school, which is the best way for them to move up the economic ladder,” said Mr. Alexander, ranking Republican on the Senate Health, Education, Labor and Pensions Committee. Mr. Paul also serves on that panel.